The Bridges selections that I observed this week were from a fashion show (2024). There were many textiles that were sewn and jewelry pieces that were 3-D printed. I chose to explore the mathematical pattern behind this earring and necklace set that was 3-D printed by Hasuna Designs:
The set displays the apollonian packing mathematical pattern. This pattern is a fractal, starting with three circles tangent to each other, then a smaller circle goes into the triangle-like space in between. There can be many variations of the pattern, depending on the orientation of first three circles as illustrated by Holly (2021):
In trying to recreate this pattern, I tried a few different things. First, I thought I might be able to use coins or buttons but the spaces became too small to fill. Second, I tried to drill with different sized bits through a scrap piece of wood, but it was too difficult to plan the radii that I needed. With a little frustration, I settled on plan number three, which was to take paper strips and tape them into rings. This allowed me the flexibility I needed to create the correct sized circles for each space. The tape warped the circles a bit, but I am happy with the results which are now hanging on my white board in my classroom awaiting curious questions tomorrow (I hope!)
One theme that resonated with me this week between this activity and Vi Hart’s videos was play. In working with the pattern, I tried many things. Some that did work, some that did not. There was a playfulness about this approach. What happens if I do this? Would this work? It took time, and I feel fairly well acquainted with the apollonian circle packing pattern now. I was wondering if recreating something would lead to as much learning as creating something new. I think it did.
References:
Holly, J. E. (2021). What type of Apollonian circle packing will appear? The American Mathematical Monthly, 128(7), 611–629. https://web.colby.edu/janholly/files/2021/11/Holly21pdf.pdf
I appreciate how honestly you described the trial‑and‑error process in recreating the Apollonian packing. Your willingness to experiment with different materials, and then adapt when things didn’t work, captures the playful, exploratory spirit you noticed in Vi Hart’s videos. I also loved the idea of hanging the finished piece in your classroom; it turns your learning into an invitation for curiosity and conversation. Your reflection on whether recreating can lead to deep learning resonates strongly here, it’s clear that through making, testing, and revising, you developed a meaningful understanding of the pattern and its structure.
ReplyDeleteThank you, Nichola and Fiona! Nichola, I appreciate your persistence and playful, experimental approach, and I think that the resulting artwork is really beautiful. I completely agree that the exploration (including some tries that don't work) is what deepens the understanding. Great stuff! (And BTW I have a pair of Christopher Hanusa's Apollonian Gasket earrings that I bought at his booth at a recent Bridges conference -- so nice to wear and contemplate!)
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